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%I #21 Aug 16 2018 12:24:40
%S 1,10,23,57,776,333,240,8121,17946,2916,800,44608,200961,176160,16725,
%T 2226,168675,1124208,1995852,1045050,70911,5390,501528,4281300,
%U 11198720,11877825,4485960,241913,11712,1261701,12773538,42697300,66700400,51044337,15385706,701968,23355,2807296,32195646,127461216,254387500,286724160,175153881,44761216,1798281,43450,5685903,71718336,321364540,759518850,1093653675,983988208,509689776,114826410,4173775
%N Non-isomorphic colorings of the cube under rotations, using at most N colors on the faces and M colors on the vertices. Square array H(N,M) with N,M > 0 read by antidiagonals.
%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2828924/">coloring cube sides and vertices</a>
%F H(N,M) = (1/24) (N^6 M^8 + 6 N^3 M^2 + 3 N^4 M^4 + 8 N^2 M^4 + 6 N^3 M^4).
%F Cycle index is (1/24)*(a1^6 b1^8 + 6 a1^2 a4 b4^2 + 3 a1^2 a2^2 b2^4 + 8 a3^2 b1^2 b3^2 + 6 a2^3 b2^4).
%e Square array begins:
%e 1, 10, 57, 240, 800, ...
%e 23, 776, 8121, 44608, 168675, ...
%e 333, 17946, 200961, 1124208, 4281300, ...
%e 2916, 176160, 1995852, 11198720, 42697300, ...
%Y H(N,1) (first row) is A047780. H(1,M) (first column) is A000543.
%K tabl,nonn,easy
%O 1,2
%A _Marko Riedel_, Jun 24 2018